I don't recall the manga or databook saying she left her homeworld to avoid them. The db said the otsutsuki clan were searching for the chakra fruit, that's it.
I think you are right, I like the idea that she arrived on Earth because it was her mission to collect the Earth fruit, she fell in love for the first time (Ootsutsuki eat each other, they don't know what love is), so she decided to stay on Earth, and when she felt huge Pain for the first time, she ate the fruit and became crazy.
If Kaguya was a princess, she must be the daughter of a king, a king rules over lots of people, implying that Kaguya comes from a populated planet, even if everyone is a Ootsutsuki there, they must be a lot to call Kaguya a princess.
I like this idea:
The Ootsutsuki leader, the king, controls Kaguya, Momo and Kin actions (and many more).
The Ootsutsuki leader sends shinjus on planets and every thousand year, he sends some strong members of his army to harvest the fruits.
Kaguya got the privilege (she is a princess) to look after a big fruit of a big planet full of energy, unlike Momo and Kin who were restricted to little planets.I say that because Momo and Kin got beat by a fraction of the Earth fruit power (Naruto+Sasuke+Boruto), Earth fruit>>>>Momo and Kin's planet fruit, making Kaguya>>>>Momo and Kin.
But Kaguya didn't follow the leader's plan, she stayed on Earth because she fell in love, ate the fruit, became crazy and planned to use its powers for her future plans, create a new dimension.
Seing that Kaguya didn't come back, the king contacted Momo and Kin (they were on a planet next to Earth) to tell them to go look after Kaguya and the Earth fruit.
That would explain that Kaguya feared someone, as I hardly see Kaguya lose against Momo and Kin.She feared that the leader would have sent someone very strong to look after her, Momo and Kin being just harvest men of little planets, they may be weaker than other members.